Reproduce “Wasserstein Exponential Kernels” on OpenResearch
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About this paper
Henri De Plaen, Michaël Fanuel, Johan A. K. Suykens
Researchers from KU Leuven developed Wasserstein exponential kernels that leverage optimal transport theory to measure similarity between structured data points more effectively than traditional Euclidean distances. Their methods demonstrate reduced classification errors on small training datasets for shape and image recognition tasks, outperforming standard Gaussian RBF kernels and kNN classifiers.
Key insights
- The existence of a bandwidth parameter σ_PSD > 0 ensures any symmetric distance-based squared exponential kernel matrix becomes positive semi-definite for σ ≤ σ_PSD, providing a theoretical foundation for kernel validity.
- Wasserstein feature maps offer a practical method to construct a guaranteed PSD kernel by truncating the spectral decomposition to include only strictly positive eigenvalues.
- Least Squares Support Vector Machines (LS-SVMs) can exhibit surprising robustness to potentially indefinite kernel matrices, with the direct 'Indefinite Wasserstein' kernel achieving strong performance in practice.
Summary by alphaXiv.
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